Nernst Equation Calculator
Potassium at 5 mM outside and 140 mM inside gives an equilibrium potential of -89.0587 mV at body temperature, close to the resting membrane potential.
-89.0586940381457 mV
Full answer, then cut to fewer decimals (not rounded):
- -89.0586940381457 mV
- -89.058694038145 mV
- -89.05869403814 mV
- -89.0586940381 mV
- -89.058694038 mV
- -89.05869403 mV
- -89.0586940 mV
- -89.058694 mV
- -89.05869 mV
- -89.0586 mV
- -89.058 mV
- -89.05 mV
- -89.0 mV
- RT/zF
- 26.72665911 mV
- Slope per tenfold change (2.303 RT/zF)
- 61.54040686 mV
Step-by-step solution
- E = (RT ÷ zF) ln([out] ÷ [in]), T = 310.15 K
- E = 26.72665911 mV × ln(5 ÷ 140) = -89.05869404 mV (inside relative to outside)
Nernst Equation Formula
E = (RT/zF) ln([C]ₒᵤₜ/[C]ᵢₙ)
R = 8.314 J/(mol·K), F = 96,485 C/mol, z the ion’s valence; 61.5 mV per decade at 37 °C for z = 1
Worked Example
Potassium with 5 mM outside and 140 mM inside the cell at 37 °C:
- E = (RT ÷ zF) ln([out] ÷ [in]), T = 310.15 K
- E = 26.72665911 mV × ln(5 ÷ 140) = -89.05869404 mV (inside relative to outside)
Slope per tenfold change (2.303 RT/zF): 61.54040686 mV
GATE tip
At 37 °C, RT/F = 26.7 mV and 2.303RT/F = 61.5 mV: a tenfold concentration ratio gives 61.5/z mV. Electrodes such as pH and ion-selective sensors follow the same Nernst slope.
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Frequently asked questions
Why is the potassium potential close to the resting potential?
At rest the membrane is far more permeable to K⁺ than to other ions, so the membrane potential sits near E_K. The Goldman equation weights each ion by its permeability.
What sign convention is used?
E is the inside potential relative to the outside. Positive ions more concentrated inside give a negative E.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Nernst Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/nernst-equation-calculator/
IEEE
Scientific Converters, "Nernst Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/nernst-equation-calculator/